CHAPTER 13 - INTRODUCTION TO GRAPHS

EXERCISE 13.2

1. Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples
Number of apples 1 2 3 4 5
Cost (in ₹) 5 10 15 20 25

This is a linear graph showing a direct proportion between the number of apples and their cost.

0 1 2 3 4 5 Number of apples 0 5 10 15 20 25 Cost (in ₹)
(b) Distance travelled by a car
Time (in hours) 6 a.m. 7 a.m. 8 a.m. 9 a.m.
Distances (in km) 40 80 120 160

This is a linear graph showing a direct relationship between time and distance.

6 am 7 am 8 am 9 am Time (in hours) 0 40 80 120 160 200 Distance (in km)
(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m?

Looking at the graph, the distance at 7:30 a.m. is 100 km and at 8:00 a.m. it is 120 km. The distance covered is \(120 - 100 = 20\) km.

(ii) What was the time when the car had covered a distance of 100 km since it’s start?

According to the graph, the car had covered 100 km at 7:30 a.m.

(c) Interest on deposits for a year.
Deposit (in ₹) 1000 2000 3000 4000 5000
Simple Interest (in ₹) 80 160 240 320 400

This is a linear graph showing a direct relationship between the deposit and the simple interest.

0 1000 2000 3000 4000 5000 Deposit (in ₹) 0 80 160 240 320 400 Simple Interest (in ₹)
(i) Does the graph pass through the origin?

Yes, the graph passes through the origin. When the deposit is ₹0, the simple interest is also ₹0.

(ii) Use the graph to find the interest on ₹2500 for a year.

The interest on a deposit of ₹2500 is ₹200.

(iii) To get an interest of ₹280 per year, how much money should be deposited?

To get an interest of ₹280, a deposit of ₹3500 should be made.

2. Draw a graph for the following.
(i)
Side of square (in cm) 2 3 3.5 5 6
Perimeter (in cm) 8 12 14 20 24
Is it a linear graph?

Yes, it is a linear graph. The relationship between the side and the perimeter is directly proportional (\(P = 4s\)).

0 2 3 3.5 5 6 Side of square (in cm) 0 8 12 14 20 24 Perimeter (in cm)
(ii)
Side of square (in cm) 2 3 4 5 6
Area (in cm\(^2\)) 4 9 16 25 36
Is it a linear graph?

No, it is not a linear graph. The relationship between the side and the area is not a direct proportion (\(A = s^2\)).

0 2 3 4 5 6 Side of square (in cm) 0 4 9 16 25 36 Area (in cm\(^2\))

NCERT Class 8 Mathematics (2024-25 Edition)